On Thursday, December 26, 2024 at 6:00:14 AM UTC-7 Alan Grayson wrote:
On Thursday, December 26, 2024 at 3:26:41 AM UTC-7 Alan Grayson wrote: On Thursday, December 26, 2024 at 12:12:43 AM UTC-7 Jesse Mazer wrote: On Wednesday, December 25, 2024, Alan Grayson <[email protected]> wrote: On Wednesday, December 25, 2024 at 5:14:21 PM UTC-7 Jesse Mazer wrote: On Wednesday, December 25, 2024, Alan Grayson <[email protected]> wrote: *Why do refer to transformations that don't preserve time ordering? IIUC, such transformations only occur when assuming motion faster than light. * No, that’s not correct. Motion faster than light would be required if there was a claim of causal influence between events with a spacelike separation; but there’s no such claim here; in both Brent’s example and mine, if we consider the event A of the back of the car passing the front of the garage and the event B of the front of the car reaching the back of the garage, there is a spacelike separation between those events, and neither event has a causal influence on the other. *I'm asking a general question. Why do you refer to failure of time ordering? What was the point you thought you were making? AG* Because as you previously agreed, the question of whether the car fits reduces to the question of whether the event A = back of car passes front of garage happens before, after, or simultaneously with the event B = front of car reaches back of garage. Since these events have a spacelike separation in both Brent’s and my numerical examples, in relativity different frames can disagree on their order, that’s the whole reason we say frames disagree on whether the car fits. *As I recall, you were writing about the failure of TIME ordering, and this would mean violation of causality, not what we're discussing on this thread. AG * You either recall incorrectly or misunderstood at the time, but disagreement about the time ordering of two events A and B does NOT imply any violation of causality; it just implies the spacetime interval between A and B is spacelike, but normally this is combined with the assumption that there are no causal influences between events with a spacelike separation. Do you understand what the spacetime interval is? If I gave you the difference in time coordinates T = tB - tA for the two events along with the difference in position coordinates X = xB - xA, would you know how to calculate the spacetime interval and judge whether it is timelike, spacelike or lightlike? *But if so, you're not within the postulates of SR, which is what this discussion is about. So what point do you think you're making? AG* *Re: paradox: Assume there's an observer located in the garage. This observer is in the garage frame. This observer sees the car easily fit in the garage. Imagine another observer riding in the car. This observer is in the car frame and observes being in the garage but never fitting in the garage. What are the observations when the two observers pass each other, in juxtaposed positions?* I’ve asked this before, but by “see” do you mean in terms of when the light from different events reaches their eyes, or something more abstract like a computer animation they create of when events occur in their frame, once they have measured the time and position coordinates of all events using local readings on rulers and clocks at rest relative to themselves? *Nothing more abstract. One observer sees the car sticking outside the back of garage, the other sees it inside, when both are juxtaposed. * You didn’t quite answer my question—you are just talking about what they see with their eyes, right? *I used the word "see". Is this not clear enough? AG* Not entirely, since it’s routine in relativity problems to use words differently from everyday speech, for example in ordinary speech when you talk about “observing” some event we are usually talking about visual sight, but in relativity talking about what someone “observes” always refers to how things happen in the coordinates of their frame, not to visual sight. If so, there is no disagreement between observers passing through the same point in spacetime about whether the car fits in a visual sense. *Really? So if the garage is 10' long in rest frame, * Do you mean 10’ in the garage’s rest frame? As I said before, just using “rest frame” without specifying a particular object is unclear. *What could be the meaning of "rest frame" associated with "garage"? I don't have a clue. Shall we consult Webster's Dictionary? As for my numerical example, I suggest you do the arithmetic, and if you don't get my prediction, I will concede the argument. AG * *Yeah, use 12' and 10' for the lengths of the car and garage respectively when at rest (which means no motion of car). Then using the LT determine how fast the car must be moving to contract the car's rest length to .000001' from the pov of the garage frame. Then place the car in the center of garage, and recognize how easily it fits (by any method of your choice). Now, from the pov of the car frame, and the speed of the car previously calculated, calculate the contracted length of the garage, and place the car at the center of the garage. Does the front of the car extend beyond the rear of the garage, whereas previously it did not? No need to worry about what "seeing" means in this comparison. Since we have two observers in this scenario, one in each frame, one riding in the car who is located at the comparison point in garage, at its center, and the other at the center of garage, we can consider the observers as juxtaposed, at the same location in spacetime. AG* *The juxtaposed spacetime events of comparison will have different labels, since they're from different frames. But physically they're co-located with different physical measurements. This result, I claim, defeats your claim that local measurements are frame independent. AG * *and car is .00001' long in garage frame when car is moving, and car is, say, in center of garage, the observer in car frame, residing inside car, won't observe his car just won't fit in garage because of huge contraction of garage in car frame, when both observers are juxtaposed, presumably at the same point in spacetime?* You would have to specify more details, like the rest length of the car and the relative velocity of car and garage and the location of the observers, in order to determine whether both observers at that point see it fit or both observers see it not fit. But suffice to say *if* an observer at rest relative to the garage is visually seeing the car fit when the observer is passing through a given point in spacetime, then an observer at rest relative to the car who is passing through that same point in spacetime is also visually seeing the car fit (even if the car does not fit in terms of local position and time measurements in his frame), this is a straightforward consequence of all frames agreeing about local configurations of photons at a single location in spacetime. I could give a numerical example at some point to illustrate this, but if you couldn’t follow my earlier numerical example I doubt this would be clear to you either, which is why I suggest it would be a good idea to return to my last response to one of your “?” responses on that example and continue from there. Jesse -- You received this message because you are subscribed to the Google Groups "Everything List" group. 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